In November 2015, the Rolling Stones were at Mark Knopfler’s British Grove Studios, in London, to record an album of new material. Things were not off to a good start. Keith Richards told Rolling Stone that he thought, “The room is fighting me. It’s fighting the band. The sound is not coming.” Richards suggested that they play “Blue and Lonesome,” a song by blues harpist Little Walter from 1959. Everything clicked and, as Richards described it, “a sound is happening and it was good.”

The Stones didn’t end up recording any Jagger-Richards tunes, and their new album, Blue & Lonesome, is a reminder that the world’s greatest rock’n’roll band is, at its core, a blues band. In three sessions they cranked out versions of 12 blues tunes originally recorded by Howlin’ Wolf, Otis Rush, Willie Dixon, and others. Little Walter is represented by four selections, and Jagger’s harp playing in the title track is truly fierce, a reminder of his command of the instrument and his deep understanding of the music that inspired him and his band.

Jagger’s harp opens the album in Little Walter’s “Just Your Fool,” with Richards and Ronnie Wood playing dark, dense rhythm guitar behind him, and Charlie Watts solidly holding down the beat. Darryl Jones on bass, Chuck Leavell on piano, and Matt Clifford on Wurlitzer piano fill things out, but the track is lean and basic -- there’s nothing superfluous or fancy, and plenty of space for the music to move around in.

Richards and Wood lock together in Jimmy Reed’s “Little Rain,” and Watts sneaks in with simple brush taps on snare. Jagger’s harp solo isn’t flashy, but every note is precise and moving, and his tone is both elegant and brutal. In 1966, when the Stones were about to release their sixth UK album, Aftermath, Howlin’ Wolf recorded “Commit a Crime.” To hear the original and then this new version is to understand how much the Stones learned from Wolf.

Eric Clapton plays slide in Little Johnny Taylor’s “Everybody Knows About My Good Thing” and Willie Dixon’s “I Can’t Quit You Baby,” a hit for Otis Rush. In both cases, he contributes to the overall feel of the song without doing a star turn. As a result, he sounds more relaxed and fiery than he did even on his most recent solo album.

The playing on Blue & Lonesome is impressive from start to finish, but Jagger shines. His mastery of blues harp has never before been so prominently displayed, and it’s clear that he’s a forceful, inventive player. Returning to these old blues tunes also lets him turn in some of his most honest and heartfelt singing. He seems to have been able to put aside his persona as a Rolling Stone and relax into these songs, and the result is some of his least mannered singing.

Unlike some of the Stones’ records since Tattoo You (1981), which have had their moments but in the end sounded like recordings made to meet a contractual obligation, Blue & Lonesome sounds like the work of a real band. By going back to songs that were, in most cases, recorded when they were kids, they’ve been rejuvenated. Keith Richards and Ronnie Wood lock together, their guitars biting and snarling; the songs are played with real conviction; and Charlie Watts, always the most steady and honest element in the band, is inspired and in the pocket.

The sound isn’t as atmospheric as, say, the recordings the Stones did at Chess Studios in 1964, but it has just enough dirty edge to make these songs sound as they should.